Square or rectangular containers allow maximum use of available pallet, shelving, and warehouse space and therefore are often preferred by manufacturers. However, because square or rectangular plastic containers and covers made from high density polyethylene (HDPE) or polypropylene (PP) have traditionally performed poorly in industry standard drop, stack, and leak tests, their use has generally been restricted to non-hazardous dry goods. This poor performance is primarily due to design constraints associated with the product shape. Latching features can be easily molded into the straight sidewalls, but the abrupt change in skirt direction at each of the four corners has historically prevented adequate latching features from being molded at these locations. Traditionally, covers are stripped out of a mold. The typical square or rectangular covers, however, cannot be so stripped at the corner because the radius is too small. The compensations necessary result in weakened corners for latching purposes and lead to leakage problems. Accordingly, there is a need for a container and lid system with a superior leak control design that can be used for square or rectangular containers.